The static frequency vs. temperature characteristic of quartz crystal resonators are discussed by, for example, Rudolph Bechmann in the Proceedings of the IRE, November 1956, at pages 1600 to 1607. Bechmann shows that the frequency vs. temperature of AT-type resonators can be described by the equation EQU (f-f.sub.i /f.sub.i)=.DELTA.f/f=A.sub.i (T-T.sub.i)+C.sub.i (T-T.sub.i).sup.3 (1)
where f is the frequency of the resonator at temperature T, T.sub.i is the inflection temperature, f.sub.i is the frequency at T.sub.i and .DELTA.f=f-f.sub.i. T.sub.i, A.sub.i and C.sub.i are constants that are functions of the angles of cut of the resonator. For a particular resonator design, T.sub.i is substantially a constant.
The thermal transient characteristics of resonators are discussed, for example, by John A. Kusters in the Proceedings of the 31st Annual Symposium on Frequency Control, 1977, at pages 3 to 7. Kusters compares the thermal transient characteristics of AT and SC-cut resonators. (Kusters refers to the SC-cut as the "TTC-cut".) He shows that the SC-cut is subject to a substantially smaller thermal transient effect than the AT-cut.
Thermal hysteresis has been discussed, for example by Hammond, Adams and Benjaminson in the Proceedings of the 22nd Annual Symposium on Frequency Control, 1968, at pages 55 to 66.
Heretofore, the measurement of the thermal properties of a resonator have involved time consuming and costly techniques. For example, the static frequency vs. temperature characteristic has been measured by placing the resonator in an oven and varying the temperature of the oven while monitoring the frequency. The thermal transient or warmup characteristic has been measured by placing the resonator into an oven controlled oscillator and monitoring the frequency of the oscillator during warmup. The thermal hystersis has been measured by either placing the resonator into an oscillator, and monitoring the frequency during temperature cycling of the oscillator or by placing the resonator in a .pi.- network and monitoring the resonator frequency while the resonator -.pi. network combination was temperature cycled.
A measurement system that is suitable for measuring both the static frequency vs. temperature and thermal hysteresis characteristics of resonators has been discussed by Marvin E. Frerking in the Proceedings of the 23rd Annual Symposium on Frequency Control, 1969, at pages 92 to 101.
In the past, resonators often exhibited "activity dips" which necessitated a great deal of costly testing. Activity dips, and a method of testing for activity dips using an "ovenless activity dip tester," are discussed by Ballato and Tilton in the Proceedings of the 31st Annual Symposium on Frequency Control, 1977, at pages 102 to 107.